Is there any point to the 12 times table?

>> If we were really smart, we'd switch from base 10 to base 12

But I only have 10 fingers!

On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing.

You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.

Due to some airline delays, I was trying to schedule a new flight. I ended up showing a boarding pass to an attendant at the booth and asking something along the lines of "I'd like to make this connection". The ticket said departure "22.17". She asked me "What's that in `real` time?".

Two more from the garden center:

I was looking for a pump for an ornamental pond, and the pumps were advertised by the amount of gallons of water they displaced per hour. I didn't know the conversion between ft3 and gallons and I didn't have my phone so I couldn't look it up. I told one of the attendants my pond was about 60 cube feet, and asked if she could help me look up how much gallons that was. She said; "I don't do numbers like that. The only numbers I know how to count is money wink". Weird. I tried to explain; all I need is the conversion factor. To no avail. I just ended up buying the biggest one. My neighbors complimented me on how soothing that burbling water is when they go to bed. Passive aggressive jerks :)

I wanted some dirt delivered for a raised flower bed. I needed about 30 cube feet. The voice on the phone told me they only deliver by the scoop (from that big shovel on their bulldozer). Fair enough, but I asked if he had more or less an idea how large such a scoop was, in some unit I could understand, since I didn't want to end up with too much dirt. He was pretty curt in his response; "We're not going to start do that, all those units and measurements, we only do scoops". Wait what, like, how do landscape architects do this? Are scoops a thing?

I asked people if it was unreasonable to expect more in each situation. Most of them were along the lines; "yes, you're being obnoxious, just get the damn scoops".

There is some use in knowing subsets of the time tables beyond 9: specifically M x N combinations For instance, if you know that 8x12 = 96, you know that 1/12 is approximately 0.08. And since 0.96/12 is exactly 0.08, you know that the remainder is 0.04/12 which gives you the .003333... in 0.0833333...

Essentially, it supports numeric intuition.

These higher times tables can be useful in long division. In long division you have to form hypotheses about how many times the divisor goes into the partial dividend, to extract the next digit of the partial quotient. So for instance, something like this comes up:

      ________ 
  12 | 980

Now 12 doesn't go into 9, so we try 98. How many times does 12 go into 98? If you know your 12x12 times table by rote, you might realize in a flash that 12x8 is 96, so put down an 8.

If you memorized all times tables up to 99, you could so long multiplication in base 100:

       1234
       4567
       ----

You would instantly know that 67 x 34 is 2278, so ... put down the 78 and carry the 22:

       1234
       4567
       ----
       22
         78

and then 67 x 12 is 804. Bring down the 22 into it and we get 826:

       1234
       4567
       ----
      82678

Damn, that was fast! :) Then we keep going with the 45 similarly: and we can move by two places to the left. 45 x 34 = 1530; put down 30; carry 15:

       1234
       4567
       ----
      82678
     15
       30

and then 45 x 12 = 540, plus carry is 555:

       1234
       4567
       ----
      82678
    55530
    -------
    5635678
 

Totally awesome, and we only had to memorize 4950 product combinations from 1x1 to 99x99. Contrast that with plodding through it one digit at a time, with four partial product rows to then add together.

There's lots of questions thrown up by this. If people need to know times tables, do they also need to know powers of 2? They come up quite often if you deal with computers. What about squares? Anyone doing polynomials later on will be using them constantly.

My sense is you will end up memorising the things that come up anyway, so why be so strict? You'll end up teaching kids that math is a memory game.

So for fun, what do I remember, off the top?

210 = 1024. Anything higher I keep doubling.

132 = 169, biggest non derived square in my head. 1 more than 7 * 24 (hours in a week).

86400 = secs in a day?

Large prime number... 10243 (Useful for demonstrating Diffie Hellman on paper)

Ramanujan's Cab... argh... is it 1729?

3.14159 (Guess I'm not winning any contests)

2.71 (See above)

6E23

Add your own random numbers that are in your head.

Use something like 12/24/48 (US) or 48/12/24 (UK) if you want to "force" compliance, then you'll at least have an easy sanity check for each field.

The other benefit is you can check Y2038 compliance at the same time, but you should at least specify 4-digit years for whatever you're spec'ing, so you don't create the next Y2K.